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chore: to_additive various results on groups, group actions (#20547)
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Two adjustments to  #20498 that had been requested by Yaël but hadn't been implemented on time before merge.
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AntoineChambert-Loir committed Jan 7, 2025
1 parent 01e6638 commit db72aff
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Showing 2 changed files with 10 additions and 11 deletions.
6 changes: 3 additions & 3 deletions Mathlib/GroupTheory/GroupAction/Blocks.lean
Original file line number Diff line number Diff line change
Expand Up @@ -311,7 +311,7 @@ theorem isBlock_subtypeVal {C : SubMulAction G X} {B : Set C} :
rw [← SubMulAction.inclusion.coe_eq, ← image_smul_set, ← image_smul_set, ne_eq,
Set.image_eq_image C.inclusion_injective, disjoint_image_iff C.inclusion_injective]

theorem _root_.AddAction.IsBlock.of_addsubgroup_of_conjugate
theorem _root_.AddAction.IsBlock.of_addSubgroup_of_conjugate
{G : Type*} [AddGroup G] {X : Type*} [AddAction G X] {B : Set X}
{H : AddSubgroup G} (hB : AddAction.IsBlock H B) (g : G) :
AddAction.IsBlock (H.map (AddAut.conj g).toAddMonoidHom) (g +ᵥ B) := by
Expand All @@ -330,7 +330,7 @@ theorem _root_.AddAction.IsBlock.of_addsubgroup_of_conjugate
erw [AddAut.conj_apply]
simp

@[to_additive existing AddAction.IsBlock.of_addsubgroup_of_conjugate]
@[to_additive existing]
theorem IsBlock.of_subgroup_of_conjugate {H : Subgroup G} (hB : IsBlock H B) (g : G) :
IsBlock (H.map (MulAut.conj g).toMonoidHom) (g • B) := by
rw [isBlock_iff_smul_eq_or_disjoint]
Expand All @@ -353,7 +353,7 @@ theorem _root_.AddAction.IsBlock.translate
AddAction.IsBlock G (g +ᵥ B) := by
rw [← AddAction.isBlock_top] at hB ⊢
rw [← AddSubgroup.map_comap_eq_self_of_surjective (G := G) ?_ ⊤]
· apply AddAction.IsBlock.of_addsubgroup_of_conjugate
· apply AddAction.IsBlock.of_addSubgroup_of_conjugate
rwa [AddSubgroup.comap_top]
· exact (AddAut.conj g).surjective

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15 changes: 7 additions & 8 deletions Mathlib/GroupTheory/GroupAction/SubMulAction.lean
Original file line number Diff line number Diff line change
Expand Up @@ -154,21 +154,20 @@ end OfTower

end SetLike

/-- A SubMulAction is a set which is closed under scalar multiplication. -/
structure SubMulAction (R : Type u) (M : Type v) [SMul R M] : Type v where
/-- The underlying set of a `SubMulAction`. -/
carrier : Set M
/-- The carrier set is closed under scalar multiplication. -/
smul_mem' : ∀ (c : R) {x : M}, x ∈ carrier → c • x ∈ carrier

/-- A SubAddAction is a set which is closed under scalar multiplication. -/
structure SubAddAction (R : Type u) (M : Type v) [VAdd R M] : Type v where
/-- The underlying set of a `SubAddAction`. -/
carrier : Set M
/-- The carrier set is closed under scalar multiplication. -/
vadd_mem' : ∀ (c : R) {x : M}, x ∈ carrier → c +ᵥ x ∈ carrier

attribute [to_additive] SubMulAction
/-- A SubMulAction is a set which is closed under scalar multiplication. -/
@[to_additive]
structure SubMulAction (R : Type u) (M : Type v) [SMul R M] : Type v where
/-- The underlying set of a `SubMulAction`. -/
carrier : Set M
/-- The carrier set is closed under scalar multiplication. -/
smul_mem' : ∀ (c : R) {x : M}, x ∈ carrier → c • x ∈ carrier

namespace SubMulAction

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